I am doing Survival Analysis with interval-censored data and I want to apply Turnbull's nonparametric estimator to the analysis of the covariates (suggested by Turnbull (1976)).

I want to know if there anyone knows any statistical package in R wich produces the survival curve estimate based on Turnbull´s algorithm.

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#### Best Answer

If you want the Non-Parametric Maximum Likelihood Estimator (NPMLE) (what Turnbull 1976's algorithm computes), you could use the `interval`

package.

I believe the default uses the standard EM algorithm as presented by Turnbull…but this is just about the slowest algorithm out there for computing the NPMLE. This could be a problem with n > 500, for example (also depends on the number of unique interval times). In `interval`

, you can chose other faster algorithms with the `initfit`

option; for example, I believe currently the fastest option would be to set `initfit = 'initcomputeMLE'`

. The package also includes various plotting and testing functions.

Currently, the fastest algorithm available is `ic_np`

in the `icenReg`

package (note: this is the author). This can be fit as

`npmle_fit <- ic_np(cbind(l, r) ~ 0, data = myData)`

(where l and r are variables for the left and right side of the intervals in the dataset myData). And the plot can be produced by

`plot(npmle_fit)`

However, this is currently not compatible with the `interval`

functions, which can do a lot more with the NPMLE than just plot it. So unless speed is *really* a huge issue, you may want to stick with `interval`

.

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